Changes in the Budget Set

Today, we'll discuss the budget set, which represents all the combinations of two goods that a consumer can afford given their income and the prices of goods. Can anyone tell me what the budget line represents?

It shows the maximum combinations of goods a consumer can buy.

Correct! The budget line is the limit of consumption based on available income. If we know this, we can better understand how changes in income or prices will affect consumer choices. Can anyone think of what happens to the budget line if the consumer's income increases?

It will shift outward, allowing the consumer to buy more.

Absolutely right! This outward shift indicates the consumer can now afford more of both goods. Remember, we denote income as 'M'.

So what if prices change instead of income?

Great question! When the price changes, the slope of the budget line will pivot around one of the intercepts. For instance, if the price of bananas goes down, the line gets flatter, indicating that bananas are now cheaper relative to mangoes.

So, if I had to remember this, I could use 'Price Changes Pivot!'

Perfect mnemonic! Let’s recap: a change in income shifts the budget line, while a price change pivots it. Understanding this helps predict how consumers will respond in different scenarios.

Let’s get a bit deeper into how a change in income affects the budget line. If someone’s income rises, say from M to M', what happens to their consumption choices?

They can buy more of both goods!

Exactly! And when income decreases, what does that indicate for consumer choices?

They’ll have less money, so they can afford fewer goods.

Right again! When income decreases, both intercepts of the budget line decrease, leading to a parallel inward shift. Can anyone explain why the slope of the budget line remains the same during an income change?

Because the prices of the goods haven’t changed!

Correct! Keep that in mind: the slope changes only when prices change. Always remember, 'Prices impact slopes, incomes shift!'

That’s a helpful way to remember it!

Now let’s focus on how changing prices affect the budget set. If the price of one good goes up while the other's price and the consumer's income remain unchanged, how does the budget line react?

The line pivots inward, right?

Exactly! This happens because the consumer gets less of the good when its price increases. How can we mathematically show this?

We adjust the budget equation like you showed us before!

Yes, we rewrite it: p'_1x_1 + p_2x_2 = M. If p' increases, the cost of consuming that good becomes higher while the income remains the same.

And if the price decreases?

If the price decreases, the line pivots outward. So remember, 'Price decreases make more possible!'

I’ll use that to remember how price creates the pivot!